This book covers theoretical and computational aspects of non-linear shells. Several advanced topics of shell equations and finite elements, not included in standard textbooks on finite elements, are addressed. Key features include: several sets of 3D equations with the rotations introduced by either the polar decomposition equation or the rotation constraint equation; shell equations based on Reissner kinematics for finite rotations and strains, formulated in terms of different strains and stresses; a comprehensive account of finite rotations, including their properties and parameterization, as well as the algorithmic issues pertaining to rotation parameters; a comprehensive description and evaluation of several enhanced, mixed, and mixed/enhanced 4-node elements; a selection of useful remedies for such problems as: poor accuracy of in-plane shear strain, transverse shear locking, over-stiffening of warped elements, locking in sinusoidal bending, and deterioration of accuracy for extremely thin elements; a large set of numerical benchmarks for finite rotation shells; an extensive bibliography and comprehensive index. Shells have been a subject of the author’s research for years, and all the methods described in the book have been implemented and tested in the field. The book can be useful for graduate students, professional engineers, and researchers specializing in shells, Finite Elements and applied numerical methods.